Trigonometric integration

In engineering, rotational action is often translated into lineal action, or vice-versa. Sine, cosine, and tangent, are three trigonometric functions which describe lateral and transverse displacements, and their ratio, as a radius rotates through the circle it describes.

Summary of Integral Properties and Solutions

$∫sin x dx = -cos x + C$

$∫cos x dx = sin x + C$

$∫sin (ax + b) dx = -1/{a}cos (ax + b) + C$

$∫cos (ax + b) dx = 1/{a}sin(ax + b) + C$

Trigonometric substitutions

If the integrand contains a quadratic radical expression, these trig substitutions may be used: